polynomial identity

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• Polynomial — In mathematics, a polynomial (from Greek poly, many and medieval Latin binomium, binomial [1] [2] [3], the word has been introduced, in Latin, by Franciscus Vieta[4]) is an expression of finite length constructed from variables (also known as… …   Wikipedia

• Schwartz-Zippel lemma and testing polynomial identities — Polynomial identity testing is the problem of determining whether a given multivariate polynomial is the0 polynomial or identically equal to 0. The input to the problem is an n variable polynomial over a fieldF. It can occur in the following… …   Wikipedia

• Polynomial ring — In mathematics, especially in the field of abstract algebra, a polynomial ring is a ring formed from the set of polynomials in one or more variables with coefficients in another ring. Polynomial rings have influenced much of mathematics, from the …   Wikipedia

• Polynomial long division — In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division. It can be done easily by hand,… …   Wikipedia

• Polynomial matrix — Not to be confused with matrix polynomial. A polynomial matrix or sometimes matrix polynomial is a matrix whose elements are univariate or multivariate polynomials. A λ matrix is a matrix whose elements are polynomials in λ. A univariate… …   Wikipedia

• Polynomial expression — In mathematics, and in particular in the field of algebra, a polynomial expression in one or more given entities E 1, E 2, ..., is any meaningful expression constructed from copies of those entities together with (usually numeric) constants,… …   Wikipedia

• Characteristic polynomial — This article is about the characteristic polynomial of a matrix. For the characteristic polynomial of a matroid, see Matroid. For that of a graded poset, see Graded poset. In linear algebra, one associates a polynomial to every square matrix: its …   Wikipedia

• Matrix polynomial — Not to be confused with Polynomial matrix. In mathematics, a matrix polynomial is a polynomial with matrices as variables. Examples include: where P is a polynomial, and I is the identity matrix. the commutator …   Wikipedia

• Multilinear polynomial — In algebra, a multilinear polynomial is a polynomial that is linear in each of its variables. In other words, no variable occurs to a power of 2 or higher; or alternatively, each monomial is a constant times a product of distinct variables. They… …   Wikipedia

• Matching polynomial — In graph theory and combinatorics, both fields within mathematics, a matching polynomial (sometimes called an acyclic polynomial) is a generating function of the numbers of matchings of various sizes in a graph. Contents 1 Definition 2… …   Wikipedia

• Complete homogeneous symmetric polynomial — In mathematics, specifically in algebraic combinatorics and commutative algebra, the complete homogeneous symmetric polynomials are a specific kind of symmetric polynomials. Every symmetric polynomial can be expressed as a polynomial expression… …   Wikipedia